Answer:
a = 10
d = 5
Step-by-step explanation:
[tex]a_{n}=a + (n-1)d\\\\a_{5}=30\\\\a + (5-1)*d=30\\\\[/tex]
a + 4d = 30 ------------------(I)
[tex]a_{13}=70\\\\a + (13-1)d=70[/tex]
a + 12d =70 -------------(II)
Multiply equation (II) by (-1) and then add.So, 'a' will be eliminated and you can find the value of d
(I) a + 4d = 30
(II)*(-1) -a - 12d = -70 {Now add}
- 8d = - 40
Divide both sides by (-8)
d = -40/-8
d = 5
Plugin d = 5 in equation (I)
a + 4*5 = 30
a + 20 = 30
a = 30 - 20
a = 10
